For parents
Halves and quarters: explore fractions with paper
Published:
A half is one of two equal parts of a whole; a quarter is one of four. Counting pieces is not enough: their areas must be equal. Use identical rectangular sheets to make that idea visible by folding.
Agree on the whole
Take three sheets of the same size and a crayon. Keep one unfolded as a reference whole. A half of a small sheet and a quarter of a large sheet are not fractions of the same-sized whole. In this activity, the whole always means one identical rectangle. The Open University resource below illustrates fractions through paper folding.
Fold once for halves
Bring the opposite short edges of the second sheet together so they match. Press the crease and open the paper. You have two matching rectangles. Shade one and write 1/2. The 2 tells how many equal parts make the whole; the 1 counts the selected part. Fold again to check that the two parts cover each other exactly.
Fold twice for quarters
Fold the third sheet in half in the same way, then fold the folded rectangle in half again in the same direction. Match the edges. Open it to reveal four equal strips. One strip is 1/4 of the sheet. Shade two neighbouring strips to show 2/4. Four pieces are not automatically quarters: they must each have a quarter of the whole area.
Compare two quarters with a half
Place the sheet with two shaded quarters below the sheet with one shaded half and align their edges. The shaded areas match: 2/4 = 1/2. For the same whole, one quarter is smaller than one half even though 4 is larger than 2. The same area has been split into more equal parts.
Play paper orders
Pretend the rectangles are tablecloths for toys. An adult orders one half coloured or three quarters coloured; the child points to or shades the right sections on a fresh template. Swap roles so the child gives the next instruction. Before each order, point to the whole and count its equal parts. There is no need to cut the paper.
Four questions with answers
One of four equal sections is 1/4. Three shaded sections out of four are 3/4: three quarters have been selected. Two quarters cover the same area as 1/2 of the same sheet. If a whole sheet is split into two unequal pieces, neither is half of it. Let your child show each answer with paper before reading the notation together.
Common errors and further practice
If your child only counts pieces, ask whether their areas are equal. Equal-area parts can have different shapes in other partitions; the rectangles in this activity are easy to overlay. Always check that the wholes match when comparing physical amounts. A parent can later choose the Fractions book in Otto Math on iPhone or iPad. The first five routes in each book are free; further routes require Otto Plus.